1. Field of the Invention
The present invention relates to a fuzzy identification system for identifying the relationship between input and output data of a system from indefinite input and output data, and also relates to a fuzzy data processing device for processing indefinite and deviating data using an identified model.
2. Description of the Prior Art
Conventionally, the identification of a system from indefinite input/output data is realized by a fuzzy linear regression model, such as disclosed in an article "Linear Regression Model by Fuzzy Function" by H. Tanaka et al in Japanese Magazine "NIPPON KEIEI KOUGAKUSHI" vol. 25, 6, pp.162-174, 1982, or in an article "Linear Regression Analysis with Fuzzy Model" by H. Tanaka et al in IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-12, NO. 6, NOVEMBER/DECEMBER 1982.
According to these articles, the deviations between the observed values and the estimated values in a system are taken up, and such deviations are considered to be due, not to the measurement errors, but to the indefiniteness of the system structure. Therefore, the system structure is represented by fuzzy linear functions whose parameters are given by fuzzy sets. For example, if the given data are expressed as: EQU (y.sub.i, x.sub.i1, . . . , x.sub.in),
wherein i=1, 2, . . . , N
provided that y.sub.i represents a value of the ith output variable, the fuzzy linear regression model can be formulated by the following steps.
(1) The fuzzy linear model is defined by the following equation: EQU Y.sub.i =A.sub.0 +A.sub.1 x.sub.i1 +. . .+A.sub.n x.sub.in
provided that the fuzzy coefficient A.sub.i has a triangle profile which is symmetrical with respect to the center line, and has a base with a width C.sub.i.
(2) The fuzzy coefficient A.sub.i is so determined that the given data (y.sub.i, x.sub.i1, . . . , x.sub.in) are included within the estimated fuzzy value Y.sub.i having a degree greater than h.
(3) The fuzzy coefficient A.sub.i is so determined that the sum of the width of the estimated fuzzy value Y.sub.i is made minimum.
As described above, according to the prior art, the fuzzy linear regression model is formulated such that the fuzzy linear function having a fitting degree greater than a certain level with the minimum deviation is selected.
Next, a prior art example for estimating an output values with respect to inputs using regression models under two different conditions is explained. In this example, the regression models utilize multiple regression based on the method of least squares, and utilize the following two regression formulas with respect to two different conditions, respectively. EQU Y=b.sub.0 +b.sub.1 x.sub.1 +. . .+x.sub.n ( 1) EQU Y=c.sub.0 +c.sub.1 z.sub.1 +. . .+z.sub.m ( 2)
When the inputs obtained under two different conditions are (x.sub.1.sup.0, . . . , x.sub.n.sup.0) and (z.sub.1.sup.0, . . . , z.sub.m.sup.0), respectively, the estimated outputs Yx and Yz are obtained by substituting these inputs to formulas (1) and (2). From these two estimated outputs Yx and Yz, the final result Y* is obtained by taking an average between the two estimated outputs Yx and Yz, as shown below. EQU Y*=(Yx+Yz)/2 (3)
As understood from the foregoing, according to the prior art, an average is taken to obtain one result from two estimated values under two different conditions.
However, with the prior art fuzzy linear regression model, the deviations between the observed and estimated values are assumed to depend on the indefiniteness of the system structure, and thus, the system coefficients are assumed to be the fuzzy coefficients. The fuzzy coefficients are determined so as to have the fitting degree greater than a certain level with the minimum deviation. Therefore, the center of the fuzzy coefficient is always the center of the width of the fuzzy data, and is not related to the given data. Therefore, when the system is positively fluctuating, the information carried in each data may be lost.
Also, according to the prior art for estimating output values with respect to inputs using multiple regression models under two different conditions, average of the two estimated values is used as the final result. The reliability of each of the two estimated values is not always the same, but is forcibly assumed to be the same when the average is taken between the two estimated values. In other words, with the use of an average taking method, no consideration is taken to the reliability of each of the two estimated values. This results in a disadvantage in that when one of the two estimated values is abnormal while the other one is normal, the average of the two will contain abnormal information and further, it is not possible to detect the presence of such abnormal data.